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Federal Highway Administration Research and Technology
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REPORT 
This report is an archived publication and may contain dated technical, contact, and link information 
Publication Number: FHWAHRT12030 Date: August 2012 
Publication Number:
FHWAHRT12030
Date: August 2012 
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Figure 141 through figure 143 show the sensitivity of this model to CMC, w/c ratio, and age, respectively. These trends are all reasonable. Figure 141 and figure 142 show the change in compressive strength at two ages, 28 days and 1 year, which are almost at the lower and upper bounds of ages included in this model. The plot in figure 143 can be considered a strength gain curve for typical unit weight and w/c ratios used in mix designs.
The core strength data in the LTPP database were used for this model. While the materials and test ages are similar to the shortterm cylinder strength model, the compressive strength of the cores is representative of the consolidation and quality of construction in the field. An initial comparison of core versus cylinder strengths was performed to determine if there was a significant difference in two strength values. Data were matched by section and age. Data were grouped in several age categories so that strength comparisons could be made at corresponding ages. Generally, each category up to 56 days was grouped for ages of ±3 days. For ages close to 6 months to 1 year, the results were grouped for ages ±30 days. The ages at which strength test results were common to both cores and cylinders were 14 days, 21 days, 28 days, 35 days, 41 days, and 1 year.
The comparison showed that there was no significant difference between strength values determined from core or cylinder tests. The paired ttest results shown in table 25 indicate that there is no significant difference between the two strengths (P < tcritical). Figure 144, which has a trend line forced to zero intercept, shows the same results. Note that a trend line with a nonzero intercept produces a higher R^{2} (0.67), which is consistent with the Pearson correlation value of 0.82 presented in table 25.
In the development of this model, parameters similar to the cylinder strength model were evaluated. In addition, the effect of curing was considered with greater attention. However, curing did not prove to be a significant variable. As this model attempts to predict the strength up to 1 year in age, the variable accounting for age was treated in a hierarchical fashion.
Parameter 
Core 
Cylinder 
Mean 
5345.3 
5472.3 
Variance 
3,307,974.59 
3,003,561.77 
Observations 
312 
312 
Pearson correlation 
0.82 

Hypothesized mean difference 
0 

DF 
311 

tStat 
2.11 

P(T ≤ t) onetail 
0.02 

tcritical onetail 
1.65 

P(T ≤ t) twotail 
0.04 

tcritical twotail 
1.97 
This model was established as shown in figure 145.
Where:
f_{c,t} = Compressive strength at age t years, psi.
CMC = Cementitious materials content, lb/yd^{3}.
uw = Unit weight, lb/ft^{3}.
MAS = Maximum aggregate size, inch.
w/c = Water to cementitious materials ratio.
FM = Fineness modulus of fine aggregate.
t = Shortterm age in years.
The regression statistics for this model are presented in table 26. The model was developed using 294 points, and the prediction has an R^{2} value of 67.6 percent and an RMSE value of 1,122 psi. Table 27 provides details of the range of data used to develop the model. Figure 146 and figure 147 show the predicted versus measured plot and the residual plot, respectively. Figure 148through figure 153 show the sensitivity of this model to CMC, unit weight, MAS, w/c ratio, FM, and age, respectively.
Variable 
DF 
Estimate 
Standard Error 
tValue 
P_{r} > t 
VIF 
Intercept 
1 
98.92962 
1,544.34064 
0.06 
0.949 
0 
Cementitious 
1 
5.70412 
0.36589 
15.59 
< 0.0001 
1.23548 
Unit weight 
1 
28.48527 
10.59672 
2.69 
0.0076 
1.0182 
(MAS) × (w/c ratio) 
1 
2,570.13151 
538.267 
4.77 
< 0.0001 
1.2201 
Fineness modulus (FM) 
1 
199.84664 
120.68288 
1.66 
0.0988 
1.01426 
Ln(age) 
1 
611.30879 
45.08962 
13.56 
< 0.0001 
1.00026 
The model statistics for table 26 are as follows:
Parameter 
Minimum 
Maximum 
Average 
w/c ratio 
0.27 
0.69 
0.42 
Cementitious content 
376 
999 
670 
Unit weight 
120 
163 
144 
MAS 
0.375 
1.000 
0.683 
FM 
2.50 
4.37 
3.05 
Pavement age 
0.0380 
2.2160 
0.4230 
Compressive strength 
1,990 
11,350 
5,596 